Question
Volume of Cones, Cylinders, and Spheres Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
The volume of a cone is 27 cm3
. What is the volume of a cylinder that shares the same radius and height as the cone?
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
The volume of a cone is 27 cm3
. What is the volume of a cylinder that shares the same radius and height as the cone?
Answers
GPT-4o mini
The volume \( V \) of a cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
Where \( r \) is the radius and \( h \) is the height of the cone.
Given that the volume of the cone is \( 27 \, \text{cm}^3 \), we can express this as:
\[
\frac{1}{3} \pi r^2 h = 27
\]
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
Notice that the volume of the cylinder is three times the volume of the cone, since the volume of the cone is multiplied by 3 to obtain the volume of the cylinder:
\[
V_{\text{cylinder}} = 3 \times V_{\text{cone}} = 3 \times 27 \, \text{cm}^3 = 81 \, \text{cm}^3
\]
Thus, the volume of the cylinder that shares the same radius and height as the cone is:
\[
\boxed{81 \, \text{cm}^3}
\]
\[
V = \frac{1}{3} \pi r^2 h
\]
Where \( r \) is the radius and \( h \) is the height of the cone.
Given that the volume of the cone is \( 27 \, \text{cm}^3 \), we can express this as:
\[
\frac{1}{3} \pi r^2 h = 27
\]
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
Notice that the volume of the cylinder is three times the volume of the cone, since the volume of the cone is multiplied by 3 to obtain the volume of the cylinder:
\[
V_{\text{cylinder}} = 3 \times V_{\text{cone}} = 3 \times 27 \, \text{cm}^3 = 81 \, \text{cm}^3
\]
Thus, the volume of the cylinder that shares the same radius and height as the cone is:
\[
\boxed{81 \, \text{cm}^3}
\]